A correspondence between the models of Hodgkin-Huxley and FitzHugh-Nagumo revisited

Postnikov, Eugene B.; Titkova, Olga V.

doi:10.1140/epjp/i2016-16411-1

Cited by 11 publications

(6 citation statements)

References 20 publications

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“…Here, we present a systematic analysis of the Karma model comparing it to the FitzHugh-Nagumo model given that both models have been extensively used to model the behaviour of cardiomyocytes. Some additional references can be found in Beck et al (2008), Mitchell and Schaeffer (2003) for the Karma model and Barkley (1991), Biktashev (2003), Postnikov and Titkova (2016) for the FitzHugh-Nagumo model. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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Reduced Models of Cardiomyocytes Excitability: Comparing Karma and FitzHugh–Nagumo

2021

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Since Noble adapted in 1962 the model of Hodgkin and Huxley to fit Purkinje fibres, the refinement of models for cardiomyocytes has continued. Most of these models are high-dimensional systems of coupled equations so that the possible mathematical analysis is quite limited, even numerically. This has inspired the development of reduced, phenomenological models that preserve qualitatively the main feature of cardiomyocyte’s dynamics. In this paper, we present a systematic comparison of the dynamics between two notable low-dimensional models, the FitzHugh–Nagumo model (FitzHugh in Bull Math Biophys 17:257–269, 1955, J Gen Physiol 43:867–896, 1960, Biophys J 1:445–466, 1961) as a prototype of excitable behaviour and a polynomial version of the Karma model (Karma in Phys Rev Lett 71(7):16, 1993, Chaos 4:461, 1994) which is specifically developed to fit cardiomyocyte’s behaviour well. We start by introducing the models and considering their pure ODE versions. We analyse the ODEs employing the main ideas and steps used in the setting of geometric singular perturbation theory. Next, we turn to the spatially extended models, where we focus on travelling wave solutions in 1D. Finally, we perform numerical simulations of the 1D PDE Karma model varying model parameters in order to systematically investigate the impact on wave propagation velocity and shape. In summary, our study provides a reference regarding key similarities as well as key differences of the two models.

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Section: Introductionmentioning

confidence: 99%

“…Some additional references can be found in Beck et al. ( 2008 ), Mitchell and Schaeffer ( 2003 ) for the Karma model and Barkley ( 1991 ), Biktashev ( 2003 ), Postnikov and Titkova ( 2016 ) for the FitzHugh–Nagumo model. In Sect.…”

Section: Introductionmentioning

confidence: 99%

Reduced Models of Cardiomyocytes Excitability: Comparing Karma and FitzHugh–Nagumo

2021

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“…It is, really, a modification of the well-known van der Pol model [11]. The approach has been intensively used last decade (see, e.g., [12][13][14][15][16]). The model possesses the main features of the Hodgkin-Huxley model and quite accurately describes the dynamics of a biological neuron and at the same time has a relatively small computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Metric graph version of the FitzHugh–Nagumo model

Fedorov¹,

Попов²,

Popov³

2019

Nanosystems: Phys. Chem. Math.

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“…The FitzHugh -Nagumo model has been studied many times in the periodical literature. Some recent results can be found, for example, in [5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

On Integrability of the FitzHugh – Rinzel Model

Kudryashov¹

2019

Nelin. Dinam.

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The integrability of the FitzHugh-Rinzel model is considered. This model is an example of the system of equations having the expansion of the general solution in the Puiseux series with three arbitrary constants. It is shown that the FitzHugh-Rinzel model is not integrable in the general case, but there are two formal first integrals of the system of equations for its description. Exact solutions of the FitzHugh-Rinzel system of equations are given.

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A correspondence between the models of Hodgkin-Huxley and FitzHugh-Nagumo revisited

Cited by 11 publications

References 20 publications

Reduced Models of Cardiomyocytes Excitability: Comparing Karma and FitzHugh–Nagumo

Reduced Models of Cardiomyocytes Excitability: Comparing Karma and FitzHugh–Nagumo

Metric graph version of the FitzHugh–Nagumo model

On Integrability of the FitzHugh – Rinzel Model

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